Friday, December 03, 2010

Perfect SAT Math Scores: Male-Female Ratio of 2:1

Update: Mean Scores for the SAT Math Test, 2010

Males: 534

Females: 500

and Standard Deviation

Males: 118

Females: 112

In September I had a post about the 2010 Math SAT test results, and reported on the gender differences in favor of males, who scored 34 points higher on average this year than their female counterparts. This follows a persistent 30+ point differential in favor of male high school students that goes back to at least the early 1970s.

This is a follow-up to that post, and the chart above (click to enlarge) displays the results of the 2010 Math SAT test by gender for all scores between 580 and 800 by 10-point intervals. Notice that:

2. As the scores increased by 10-point intervals from 580 to 800, the male-female ratio increased in almost all cases, reaching a peak of 2.08-t0-1 for perfect scores of 800.

3. More women (827,197) than men (720,793) took the SAT test in 2010, and to adjust for those differences in sample sizes, we can calculate that 1.12% of males had perfect 800 scores compared to 0.47% of females, for an adjusted male-female ratio of 2.38:1 (vs. the 2.08 unadjusted ratio). By either calculation, there were more than twice as many male high school students getting a perfect score on the SAT Math test than female students.

As I reported before, these results are especially significant because female high school students are generally better students overall than males, and equally or better prepared for the SAT Math test than male students:

a. Females outnumbered males in the top 10% of their 2010 classes - there were 127 female students in the top 10% of high schools for every 100 male students (56% female to 44% male).

b. Nationwide, there were 144 female high school students with GPAs of A+ for every 100 males (59% female vs. 41% male).

c. Females had a higher average GPA of 3.40 compared to 3.26 on average for male students in 2010.

d. More than half of female high school students (51%) took more than 4 years of mathematics, compared to 49% of male students.

e. There were 117 female high school seniors who took AP or Honors Math for every 100 male students.

Bottom Line: Despite now being better prepared academically by many different measures, both overall and for mathematics specifically, female high school students score significantly lower on the SAT math test, and the 30-point differences in test scores favoring males has persisted since Richard Nixon was president.

And yet, we hear statements like this from the gender activists: "There just aren't gender differences anymore in math performance," says University of Wisconsin-Madison psychology professor Janet Hyde, "So parents and teachers need to revise their thoughts about this. Stereotypes are very, very resistant to change, but as a scientist I have to challenge them with data."

Given the significant and persistent differences in SAT Math tests that have persisted over many generations, and continue to be found for all ethnic groups, the scientific data about gender differences in math performance seem to be challenging Professor Hyde's fact-resistant stereotypes.

Update:Janet Hyde explains the 30-point male advantage on the SAT math test as follows, "Greater numbers of girls take the test now than boys, because more girls are going to college. So you're dipping farther down into the distribution of female talent, which brings down the average score," says Hyde. "That may be the explanation for (the results), rather than girls aren't as good at math."

But that would imply several outcomes that are not happening:

1. The average female test score should be falling over time as more girls take the SAT test and "dip farther down in the distribution of female talent." In fact, the opposite is happening - average female scores have increased over time, not decreased (see graph above).

2. If more female test-takers dip farther down in the female distribution, the male-female gap should be widening, when in fact it's been remarkably constant over time (see graph).

Further, the "dipping down the female distribution" theory would only potentially explain average test scores, and would NOT explain at all why males outnumber females by huge 2-to-1 ratios for test scores on the high end.

52 Comments:

Strong claims from MP, considering SAT data was included in the study, the authors expressly discussed & rejected MP's point, and that the study looked at a lot more data than MP did.

What is MP's precise criticism of the study? Did he he redo their analysis and find errors? Did he find fault in the statistics, or problems with the methodology?

Quote: "After sifting through mountains of data - including SAT results and math scores from 7 million students who were tested in accordance with the No Child Left Behind Act - a team of scientists says the answer is no. Whether they looked at average performance, the scores of the most gifted children or students' ability to solve complex math problems, girls measured up to boys."

Besides, the authors' preemptively rebutted MP's objection, and I would say he needs to overcome, or at least discuss, that rebuttal to his point before he goes on to restate his point like it's a knock-out.

"The study's final piece was a review of the granddaddy of all high school math tests, the SAT. The fact that boys score better on it than girls has been widely publicized, contributing to the public's notion that boys truly are better at math. But Hyde and her co-authors think there's another explanation: sampling artifact."

"For one thing, because it's administered only to college-bound seniors, the SAT is hardly a random sample of all students. What's more, greater numbers of girls take the test now than boys, because more girls are going to college."

""So you're dipping farther down into the distribution of female talent, which brings down the average score," says Hyde. "That may be the explanation for (the results), rather than girls aren't as good as math.""

The fact that more girls than boys take the SAT could explain the difference in mean test scores, but wouldn't explain the significant 2:1 differences at the high end of the distribution.

Also the ratio of female-male test-takers has increased over time, which should have decreased the average female test score, and led to an increase in the male-female average test score differences. But that has not happend, the average score differential has been almost the same for 40 years.

The claims were not backed by anything substantial in the referenced article, so it would be impossible to say this posting was rebutted. I don't consider "a team of scientists says the answer is no" to be enough evidence to draw a conclusion that it is in fact so. Perhaps a stronger case could be made if we saw the women's report and analyzed the data ourselves such as was given by Professor Perry in the chart in this posting.

I think the SAT data is overwhelming that men have historically tested better in the math portion of the SAT than women. I don't see how the data can be interpreted any differently unless you can show the data are inaccurate.

Of course, it can be debated how well any standardized test measures what it is supposed to measure (validity). I think we can let the SAT test makers prove that validity because that is their job.

Is this a debate about who's better at math or a debate a validity of the SAT? These are interesting questions, but pale before what I think is the real issue: whether the schools are teaching the subject adequately.

A year ago I helped a relative (a girl) go through some practice Math SATs. I found out that she didn't know the multiplication tables. This slowed her down on at least half the questions -- she couldn't eliminate unlikely answers without literally doing the math.

I chalk this up not to her gender, but to flaky mollycoddling educational theory. In the same vein, my son went through repeated bouts of American history without being able to name the decade of the Civil War. (He's now majoring in Math.)

"A year ago I helped a relative (a girl) go through some practice Math SATs. I found out that she didn't know the multiplication tables."

Chris, I certainly won't defend the public education system, assuming your female relative is a product of that system, but her experience can't be the norm, as evidenced by the fact that some students are acing the SAT. Students somewhere are learning the multiplication tables, and it isn't just boys.

How did your relative cope all these years since 3rd or 4th grade without knowing them? It must have been a struggle. I'm surprised she didn't ask you for help earlier to prepare her for the SAT by learning the multiplication tables.

> "That may be the explanation for (the results), rather than girls aren't as good as math."

Yes, and it could well be that increased umbrella sales are caused by porcine aerialism, but that's not generally the way to bet.

Females are, by nature, normative in society. They tend to be more tightly clustered around the medians and the means, with a lower SD than males.

Males tend consistently to have more outliers -- both more geniuses and more idiots. More passives and more aggressives. And so forth.

Feminist folderol to the contrary, this will continue to be so in sheer and utter defiance of the idea that the sexes are utterly interchangeable in all ways. There are things women -- as a group -- will always be better at than men.

There's two conflicting bits of evidence: the SAT data says that males outscore females on math and have done so for as long as we have data; but No Child Left Behind (NCLB) data, as studied by Janet Hyde and company shows no difference in math performance. How do we reconcile the contradiction?

I see two ways. On the one hand we could explain the SAT data as flawed. The argument Hyde uses is bad because males outperformed females even when more males took the test than females in the 70s. But maybe there is a sampling artifact due to distribution of math skills. It is acknowledged that male and female IQ are distributed differently, both having the same average, but males having more variance. Namely, males outnumber females in the really dumb and really smart ends, but females outnumber males around the average. Since the people taking the SAT are only roughly the smarter 50%, and if math skills are distributed like intelligence, then all the males who are profoundly bad at math are simply not taking the test, and since these would outnumber the females who are really bad at math, then the overall average scores of male test-takers is raised relative to females.

The other explanation is to say the NCLB data is flawed. The problem with the NCLB data is first of all that the math on it isn't really that hard and second that there is a lot of teaching to the test. As has been noted, females are overall much better academically than males. What we might be observing is that the females compensate for their poor math skills by studying harder. The NCLB test is just asking students to use math skills they've recently learned, whereas the SAT is actually testing math skills with surprising and challenging questions (it has been noted elsewhere that SAT prep course make very little difference in scores). Also, since the NCLB math is not too challenging (Hyde et al note the paucity of the most challenging types of math question sin their study), it doesn't really show the advantage of males, which becomes more and more obvious with more challenging and more advanced math.

Personally, I'm agnostic on this question. I think we need better data to answer it, something like the SAT, but administered to all students.

Joe, I disagree. There is more than enough data to draw conclusions. The standard deviation is smaller for females. And it looks like the male score distribution is skewed a bit toward the higher end, making it less normal (kurtosis).

That's it. You have a higher percentage of females who score higher in soe score ranges, but the tails of the distribution shift the mean higher for males. So the special interest data disecters can say one thing, when the data indicates another.

Any conflicting evidence was created by you trying to compare apples and oranges testing.

You can't draw one conclusion from two different tests because you can't assume that the SAT and NCLB are measuring the same thing at the same point in time. You would have to have the same students taking both tests if you want to do that, and even then you would have to rotate the order of the tests every-other-one to eliminate any fatigue factor.

Even if the NCLB data were comparable to the SAT, I don't think it has been around long for an accurate trend comparison.

I think you are right about everyone taking the SAT for a comparison, but I am not sure what that would mean. Real-world problem-solving does not always show up in standardized testing. I had to explain to a co-op student from a world-class engineering school (used to be GMI) that the marks on a folding ruler were each 1/16 of an inch, and she was supposed to be a math genius from India.

I think looking at the graph showing both high and low scores is instructive, i.e. boys have a higher standard deviation in their ability. On AVERAGE perhaps boys/girls have the same math ability, but at the tails of the distribution the results are very different. Boys grow up to be men, occupying more positions at the top AND at the bottom.

I can't deny that the ranks of the top math performers are predominantly male (by a large margin). As far as the political debate goes, this is enough to explain why it is that math-related fields are dominated by men. Any person who says that women are being discouraged from entering math or that there is systematic anti-female bias in math is drawing unfounded and unnecessary conclusions.

On the other hand, what I wonder is whether the distribution of math skills at the lower end is symmetrical to the distribution at the higher end, balancing things out so that on average men and women are about equal in math skills. I'm not aware of any evidence that this is not the case, and I have nothing invested in this either way, so I'll just stay on the sidelines and wait for better evidence.

Comparing it to a similar case, it seems pretty clear that women are better than men at writing. This explains why it is that journalism is dominated by women, but the greater variance in writing skills may explain the predominance of men among the truly great writers (hard to prove, I admit, but if we just look at Nobel laureates in literature we see, men: 94, women: 12 [~8:1]. If we look at the past 30 years we see a probably much less biased count, men:24, women:6 [4:1]).

Joe said, "This explains why it is that journalism is dominated by women . . ."

In what positions and media, Joe? Writers, editors, publishers, owners, newscasters, meteorologists, producers, directors . . .? I don't have data, but it doesn't seem to be what I read and see daily.

Maybe journalism/English teachers/professors are mostly women, but how do we know that the men did not score high on math, too and decided to choose the incentives in a more lucrative field? Have you seen the difference in pay between a business professor and English professor? I can write, but I can be bought.

"You can't draw one conclusion from two different tests because you can't assume that the SAT and NCLB are measuring the same thing at the same point in time.

Joe hasn't drawn one conclusion from two different tests, he has in fact, explained why the two different tests could get different results that aren't mutually exclusive, precisely BECAUSE the two tests are different.

If we accept the premise that male math ability is more broadly distributed than that of females, then the SAT, which is not usually taken by low performers, will indicate a difference at the high end favoring males, which is what the chart indicates. The NCLB test, on the other hand, which any student who hasn't slept through most of their classes can pass, doesn't challenge anyone near the tails of the curve whether male or female, so it wouldn't show this discrepancy at the high end of the math ability distribution curve.

I wouldn't favor testing all students with the SAT or something similar unless there were some demonstrable benefit to the students. Low performers and those not planning on college would be wasting their time. If the the only purpose would be to satisfy our curiosity about math ability differences between genders, then let's not do it, and instead spend the resources on something that might actually benefit students.

I read the term "it is flawed" that started the two test description paragraphs to mean that Joe stated that if the two tests do not have the same results, one of them was flawed. I understand what you are saying, but it seemed to me that Joe did think the tests should show the same results. It seemed like a lot of explanation of why the tests were different using a comparison/contrast analysis to me, and i just don't think they can be compared or contrasted.

I don't know if it should be the SAT, but I am in favor of exit testing before a high school diploma is issued. A high school diploma should denote at least a minimum amount of knowledge and not just 13 years of school survival. I am amazed every year when I have to teach how to fill out an invoice and add a 6% sales tax to college students.

"Russ Whitehurst, a former top education official in Mr. Bush's administration, noted that NCLB focuses more on early grades and wasn't designed to have a huge impact on high school. The SAT scores echo other national tests that have found improvement in early grades that don't translate into high school, he said." (Source: WSJ).

How could a program and testing that is not designed to impact high school have much to do with the SAT? Why would anyone design a school program that did not impact the terminal result of K-12 school? Strange.

Of course, I asked my wife why boys score better as an average and she said it's because the questions reference male-centric themes.

Has your wife taken much math? I ask because one of the first things good math instructors teach you about solving word problems is to separate the wording of the problem from the facts of the problem. This is both because wording is often subtly (and intentionally) misleading, and because it shouldn't matter to the test taker whether the objects in the problem are puppy dog tails or sugar and spice. Nobody who takes the SAT should be unfamiliar with the concept.

This makes me wonder whether girls have come on like gangbusters in math because current test conditions reward process more than talent. Girls are widely noted to get better grades because they're better at process. Ergo, it may be that girls as a group score better on math tests today because they per se, or the way they are administered, reward process as much as results.

I also wonder how much of the skewing of scores on SATs has affected the stats. It's well known that the SATs were changed years ago to skew just above above median scores higher in order to goose the average scores of girls. The lower the score the bigger the adjustment, which means that the highest scorers, most of whom are boys, get no benefit while those just below them, with a majority of girls, get their scores adjusted up, compared to the flatter curve used before.

It's also well known that the 2400 SAT has two verbal sections and one math, versus the old 1600 SAT with one of each, in an attempt to skew overall scores in favor of girls.

"I don't know if it should be the SAT, but I am in favor of exit testing before a high school diploma is issued."

I used to agree 100% with that, but I have changed my mind for the following reasons. a) It shouldn't be necessary, as students are tested throughout their school careers, and receive grades. They should know where they stand long before graduation. In their last six years, they take final exams for each class. Failing these should prevent advancement and ultimately deny a diploma. b) a national standard exit test can cause a great deal of 'teaching to the test', which distracts from actual learning. c) For those going to college, the SAT should be a good indicator of how well they have done to that point. d)College entrance exams should indicate to a student whether they are really prepared for the school they have applied to.

I agree that there are problems, and they need to be addressed, but if all the current tests and measurements aren't adequate, then one more test isn't likely to change anything.

Yes, she is a product of public education, and it is a public education that I can put an exact value on: our school system (Montauk, NY) pays $28,000 in tuition to the East Hampton, NY school system to send a kid to East Hampton High School.

Now, in order create the cash to pay that bill, my fellow Montaukers and I have to actually work, contribute to the GDP, rather than ensuring our sons and daughters are being taught basic arithmetic.

And that's my point. Academics and intellectuals can debate whether boys are better than girls at math until their ears fall off. It doesn't matter. It doesn't matter whether the SAT is in some mystical way skewed to favor boys. And it doesn't matter which end of the bell curve we're talking about.

I understand that many of you are engaged in an earth-shaking ideological argument. I'll leave you to it.

I don't think you can narrow it down to one specific factor. It's most likely a combination of the following broad categories.

Physiologic: Sexual dimorphism in behavior is a well documented phenomenon and it's plausible that natural selection encouraged the survival of females that for some reason do marginally worse in math. I find this extremely unlikely but it's not impossible.

Statistical: There's a tremendous amount of selection bias in who takes the SATs so it's questionable whether this is a representative sample of human society. Remember this when you try to generalize results from a specific self-selecting subset of one country to the entire human race.

Sociocultural: Social norms don't get thrown out overnight, gender equality is a relatively new idea. Women have been socialized into the role of the housewife for the vast majority of civilization so that's going to have some effect on the social structure of society don't you think?

Unlike the study, Dr Perry uses a standardized test (set nationally instead of by states) with sufficient observations (i.e. annual data since 1972) to prove males have a higher variance and a higher mean in math scores than females.

The explanation of "sampling artifact" is ridiculous. The SAT data (since 1972) show the average score of males is higher than females regardless of the ratio of males and females taking the test, and it's questionable that the entire population of college-bound students is a sample.

In Minnesota, the most commonly taken standardized college entrance exam is the ACT. Seventy percent of Minnesota high school graduates in 2010 took the assessment.

Minnesota's average composite score of 22.9 was the highest in the nation...Minnesota has led the nation in average composite ACT scores for six consecutive years. The national composite score was 21.0.

The data indicate that:

Students who take rigorous high school courses consistently perform better on the ACT.

Some states, including Colorado, Illinois, Kentucky, Louisiana, Michigan, Mississippi, Tennessee and Wyoming require all (or nearly all) of their high school seniors to take the assessment.

The ACT results are more representative of Minnesota than the SAT. Only about 10 percent of Minnesota college bound seniors take the SAT, compared to 46 percent nationally. Minnesota students taking the SAT are typically applying to selective out-of-state colleges.

Males may be just as capable as females in nursing or ballet. However, it's a question of willingness.

Nursing is not like ballet. For one thing, there is no physical impediment to a man's performance of the job. His obstacles are entirely social, ranging from disapproval of men in that role to grossly overblown fears that all men are sexual predators in waiting.

In ballet, however, men are not physically capable of doing the things women do no matter how enthusiastic they may be about ballet itself. They don't have the hips for it and are too heavy to stand on pointed toes. Social disapproval of men in ballet is just icing on the cake.

With China’s debut in international standardized testing, students in Shanghai have surprised experts by outscoring their counterparts in dozens of other countries, in reading as well as in math and science, according to the results of a respected exam.

Girls are told/encouraged simultaneously to work hard, but not to be nerds. They are also encouraged to get good grades, but play with dolls instead of legos. So, more of them take harder math classes with the subconscious idea that they shouldn't be focusing *too* much on math class.

Gender differences caused by sexism still exist; but they have changed.

Girls are told/encouraged simultaneously to work hard, but not to be nerds. They are also encouraged to get good grades, but play with dolls instead of legos. So, more of them take harder math classes with the subconscious idea that they shouldn't be focusing *too* much on math class.

Gender differences caused by sexism still exist; but they have changed.